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Transcript of tugasan hbmt 4303
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HBMT4303
FACULTY OF EDUCATION AND LANGUAGES
SEPTEMBER 2012
HBMT4303
TEACHING MATHEMATICS IN FORM FIVE
MATRICULATION NO: 810610146336002
IDENTITY CARD NO. : 810610146336
TELEPHONE NO. : 0138706454
E-MAIL : n!"#$%&'#n()"#%*+,"
LEARNING CENTRE : IPGM -#"./ Tn)/ A"./#n A&'#n
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HBMT4303
INTRODUCTION
R# & ,$#n) % #n %".!#n ,n,. %n ,#*,/*/+ I #..*%,#%n ,! #!%/ &%* %n !#* *%&
%/#%n+ I #" #! !/%! #!,$ #n !# # *# #!%,* &!" %&&!n /!, n $
#,$%n) & !# & ,$#n) #n /""#!% $ #..!#,$ / %n $ #!%,*+ I #* n .*#%n $
"#n%n) & average rate of change9 instantaneous rate of change9 #n relative rate of change+
In $% #%)n"n I $# .!.#! # & /%#:* #,$%n) #n *#!n%n) "#!%#* &! F!" 5
"#$"#%, ,*# : / %n!/, $ ,n,. & !# & ,$#n)9 # ** # #,$ $
#..*%,#%n & !# & ,$#n) %n #!%/ &%* %n !#* *%& %/#%n+ T$ "#!%#* /* ,n% &
#,$%n) #%9 #n #".* & #,%%% %n $%,$ /n %n )!/. ,#n .#!%,%.# /%n) $
"#!%#*
T$ #* !/%! / .!.#! # *n .*#n &! # %n %n #,$%n) $ .%, & !# & ,$#n)
%n $%,$ I /* / .#! ! #** & $ "#!%#* I $# .!.#!+ I $# $#! "; *n .*#n %$ #n
.!%n, F!" 5 "#$"#%, #,$! ) $ &:#, &!" $"+
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HBMT4303
SUMMARY OF APPROACH IN TEACHING RATE OF CHANGE
C#*,/*/ % $ /: #n $ #!%/ #..*%,#%n & $% ,n,.+ Nn? S,n
L# & "%n % # #"n #:/ # !# & ,$#n)@ % #; $# $ &!, #,%n) n # :;
/#* $ "# & $ :; "/*%.*% :; $ #,,*!#%n & $ :; "%n@ $n $
&!, % nn9 $ *# :," # #"n #:/ #,,*!#%n9 !# & ,$#n) & .
,".#! %"+ T$ %ffi,/*; n .!%%n) # /n n%%n & $# *,#* !# &
,$#n) !#**; #9 "# C#*,/*/ : $/)$ # /n/n :/ )%%n) ,!!, !/*9
.!$#. :,#/ !!! ,""% ! ff %n) #,$ $!F!#,%n9 !#%9 #n
.!.!%n#*%; #! .%, & "#$"#%, $# #! "#$"#%,#**; !%,$9 ,)n%%*;
,".*%,# #n %&&%,/* #,$ ="%$9 20029 .+3>+
In "#$"#%,9 # rate % # !#% :n "#/!"n %$ %&&!n /n%+1 I& $
/n% ! /#n%; %n !., & $%,$ "$%n) % ,$#n)%n) % n .,%&%9 //#**; $ !#
% per unit time+ H!9 # !# & ,$#n) ,#n : .,%&% .! /n% %"9 ! .! /n%
& *n)$ ! "# ! #n$! /#n%;+ T$ " ,""n ;. & !# % .! /n% %"9
/,$ #.9 $#! !# #n &*/+ R# $# $# # nn%" n"%n#! %n,*/ ,$#n)
!#9 *%!#,; !# #n *,!%, &*/+In ,!%:%n) $ /n% & # !#9 $ ! .! % /
.#!# $ /n% & $ "#/!"n / ,#*,/*# $ !# =&! #".* # $#!
!# % .! :# .! "%n/>+ A !# &%n /%n) n/":! & $
#" /n% =/,$ # # !#> ! ,/n =/,$ # *%!#,; !#> %** !/* %n # %"n%n*
/#n%;9 $%,$ ,#n : .! # # .!,n#) =&! #".*9 $ )*:#* *%!#,; !# %n
18 # 80> ! &!#,%n ! # # "/*%.*+
O&n !# % # ;nn;" & !$;$" ! &!/n,;9 # ,/n .! ,n =%++ H!'> +)+ !#%
&!/n,% ! $#! !# ! #".* !#+
http://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Measurementhttp://en.wikipedia.org/wiki/Rate_(mathematics)#cite_note-1http://en.wikipedia.org/wiki/Rate_(mathematics)#cite_note-1http://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Lengthhttp://en.wikipedia.org/wiki/Masshttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Fluxhttp://en.wikipedia.org/wiki/Exchange_ratehttp://en.wikipedia.org/wiki/Exchange_ratehttp://en.wikipedia.org/wiki/Literacy_ratehttp://en.wikipedia.org/wiki/Electric_fluxhttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Tax_ratehttp://en.wikipedia.org/wiki/Literacy_ratehttp://en.wikipedia.org/wiki/Dimensionless_quantityhttp://en.wikipedia.org/wiki/Dimensionless_quantityhttp://en.wikipedia.org/wiki/Percentagehttp://en.wikipedia.org/wiki/Literacy_ratehttp://en.wikipedia.org/wiki/Fraction_(mathematics)http://en.wikipedia.org/wiki/Multiplehttp://en.wikipedia.org/wiki/Rhythmhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Hertzhttp://en.wikipedia.org/wiki/Radio_frequencieshttp://en.wikipedia.org/wiki/Radio_frequencieshttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Sample_ratehttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Measurementhttp://en.wikipedia.org/wiki/Rate_(mathematics)#cite_note-1http://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Lengthhttp://en.wikipedia.org/wiki/Masshttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Fluxhttp://en.wikipedia.org/wiki/Exchange_ratehttp://en.wikipedia.org/wiki/Exchange_ratehttp://en.wikipedia.org/wiki/Literacy_ratehttp://en.wikipedia.org/wiki/Electric_fluxhttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Units_of_measurementhttp://en.wikipedia.org/wiki/Tax_ratehttp://en.wikipedia.org/wiki/Literacy_ratehttp://en.wikipedia.org/wiki/Dimensionless_quantityhttp://en.wikipedia.org/wiki/Dimensionless_quantityhttp://en.wikipedia.org/wiki/Percentagehttp://en.wikipedia.org/wiki/Literacy_ratehttp://en.wikipedia.org/wiki/Fraction_(mathematics)http://en.wikipedia.org/wiki/Multiplehttp://en.wikipedia.org/wiki/Rhythmhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Hertzhttp://en.wikipedia.org/wiki/Radio_frequencieshttp://en.wikipedia.org/wiki/Radio_frequencieshttp://en.wikipedia.org/wiki/Heart_ratehttp://en.wikipedia.org/wiki/Sample_rate
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HBMT4303
A !# & ,$#n) ,#n : &!"#**; &%n %n #;@
$! f(x) % $ &/n,%n %$ !., x ! $ %n!#* &!" a aJh+ An %n#n#n/ !#
& ,$#n) % /%#*n # !%#%+
An #".* ,n!# $ %&&!n, :n $ average #n instantaneous &%n%%n@
$ . & # ,#! ,#n : ,#*,/*#@
1+ An #!#) !# ,#n : ,#*,/*# /%n) $ #* %#n, !#** :n a #n b9 %% :;
$ !#* %"
2+ An %n#n#n/ !# ,#n : !"%n :; %%n) # ."! +
http://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Speedometerhttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Speedometer
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HBMT4303
EXPLANATION OF THE MEANINGS OF
INSTANTANEOUS RATE OF CHANGE, AVERAGE RATE OF CHANGE ,
AND RELATIVE RATE OF CHANGE.
T$ . # $%,$ # #!%#:* ,$#n) ! # .,%&%, .!% & %"+ R# & ,$#n) % &n
/ $n .#%n) #:/ ""n/"9 #n % ,#n )n!#**; : .! # # !#% :n # ,$#n) %n
n #!%#:* !*#% # ,!!.n%n) ,$#n) %n #n$!+ G!#.$%,#**;9 $ !# & ,$#n) % !.!n
:; $ *. & # *%n+ R# & ,$#n) % &n %**/!# :; $ G! *! *#+ M#n; !#! .#; ,*
#n%n $ . # $%,$ n #!%#:* ,$#n) !*#% #n$!+ F! #".*9 .%n !#!
/; $ !*#%n$%. :n $ !# & ,$#n) %n $ .!%, & #n .%n !*#% # "#** ,$#n) %n
$ .!%, & $ /n!*;%n) #9 nn # #n .%n *#+
B#%,#**;9 $ !#% & $ ,$#n) %n $ /./ #*/ #n ,$#n) %n $ %n./ #*/ & # &/n,%n
% ,#** # !# & ,$#n)+ R# & ,$#n) % $ !#% $# $ $ !*#%n$%. :n $
#!%#:* %n /#%n+ In )n!#*9 $ ,&&%,%n & x % ,#** # $ !# & ,$#n) & #n /#%n+ F!
#".*9 %n yK3 xJ49 $ !# & ,$#n) % 3+ 3 % $ ,&&%,%n & x+ In $% /#%n9 $ ,n#n
#!%#:* % 4+T$ %.*#,"n %n .%%n % nn # $ !# & ,$#n) %n .%%n+ I& # .#!%,* %
%n%%#**; # A #n #&! %" % % # $ .%n B9 $n R# & ,$#n) %n .%%n K P#!%,* # P%nBP#!%,* # P%n A T%" T#n &! C$#n) %n P%%n+
V*,%; % $ . & # .#!%,* ! :
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HBMT4303
S*. K R% & $ /#%n
R/n & $ /#%n
S*. K y2 y1
x2 x1
T$ &!"/*# &! !# & ,$#n) % )%n # &**@
R# & ,$#n) & x %$ !., y % )%n #
R# & ,$#n) & y K dx/dy
T$% % $ !*#%n$%. :n !# & ,$#n) #n *.+
INSTANTANEOUS RATE OF CHANGE
In#n#n/ !# & ,$#n) % $ *%"% & $ &/n,%n $# ,!%: $ #!#) !# & ,$#n)+ I %/ ,!%: $ #n :K2 x2J x3 # xK4+
S*/%n@
http://math.tutorvista.com/calculus/instantaneous-rate-of-change.htmlhttp://math.tutorvista.com/calculus/instantaneous-rate-of-change.htmlhttp://math.tutorvista.com/calculus/instantaneous-rate-of-change.html
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F! $ %n#n#n/ !# & ,$#n)9 ,#*,/*# $ &%! !%#% & $ )%n &/n,%n+
f = x>K4 xJ1
T$!&!9 &! %n#n#n/ !# & ,$#n) # xK4
f =4>K4 x4J1K17
AVERAGE RATE OF CHANGE
In )"!%,#* ,n,.9 $ !" !# & ,$#n) % $ *. & $ *%n #n =697> % $ ,$#n) %n $ ;,!%n# ! $
,$#n) %n $ ,!%n#9$%,$ % #* ,#** # $ *. & $ *%n+
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HBMT4303
A!#) !# & ,$#n) &!"/*# % " K y2 y1 x2 x1 $!9 " % ,#** $ *. & $ *%n #n = x29 y2>+ T$ *. & $ *%n %n $ )!#.$ K " K 7364 K 42 K 2
Hn,9 $ #!#) !# & ,$#n) & $ *%n #n =697> % 2+
A!#) R# & C$#n) F!"/*#
F! #n; .%n = x19 y1> #n = x29 y2> %n $ ,!%n# .*#n9 %& δ % $ ,$#n) %n x #n %& δ; % $
,!!.n%n) ,$#n) %n y9 $n $ %&&!n, /%n δyδx K y2 y1 x2 x1 % ,#** $ #!#) !# &
,$#n) & y %$ !., x ! $ %n!#* = x19 y1>+ I % #* ,#** # $ !#% & ,$#n) %n ;
,!%n# ! $ ,$#n) %n ,!%n#+ ,#n #%*; &%n $ #!#) !# & ,$#n) %$ $ $*.
& $ #!#) !# & ,$#n) &!"/*#+
A &/n,%n % n $! $! % # !*#%n$%. :n x #n y % n # yK f = x>9 $! x % #n
%n.nn /#n%; #n y # .nn /#n%;+
RELATIVE RATE OF CHANGE
T$ !*#% !# & ,$#n) & # &/n,%n f = x> % )%n :; $ !*#%n f = x> f = x>9 $! f = x> % $ &%!
!%#% & $ &/n,%n+
S* E#".*
/%n@ I& f = x>K3 xJ1 % $ &/n,%n+ T$n9 &%n $ !*#% !# & ,$#n) # xK1+
S*/%n@
G%n $# f = x>K3 xJ1
f = x>K3
T$ !*#% !# & ,$#n) # xK1 K f = x> f = x>
K 33 xJ1
K 33Q1J1
K 34
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HBMT4303
TEACHING & LEARNING MATERIAL AND LESSON PLAN
INVOLVING THE USE OF PREPARED TEACHING AND LEARNING MATERIAL
Mat L e ar! '!" Goa%(
R D,!%: !#*!* #..*%,#%n & !# & ,$#n) /%n) !:#* #n )!#.$%,#*
!.!n#%n9 +)+9 :/%n9 $#%n)9 ,*%n)9 "%n9 ,/!!n9 #! .!/!9
../*#%n9 n%!n"n9 !#n.!#%n+
R D,!%: ,nn,%n :n #!#) !# & ,$#n) #n %n#n#n/ !# &
,$#n) %n ,n+
Mater'a%(
R ,$#! .#.! #n "#!!
,"./! #n ## .!
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1.1.1: Revisiting Rates of Change
Co!(o%'*ate
De1r'ef
)o%e G r o $ D'( $ ( ( 'o!
S$#! &%n%n) %$ $ ,*#+ A! #n; "%/n!#n%n)+
G/%%n) /%n@
R D,!%: $ *, .%n n # ,/! $# $ *. ,#n :! !.!n $
%n#n#n/ !# & ,$#n) # #n; .%n %n $ %n!#*+
R H /* ;/ ,$#n) $ %n!#* #!/n #,$ :/n, .!% :! %n&!"#%n #:/ $
#!#) #n %n#n#n/ !# & ,$#n) & $ :#**
Pa'r( Pa'r2Sare: Fra3 er Mo*e%
A ,#,$ B %n ,".*%n) # F!#;! "* &! #!#) !# & ,$#n)+ B ,#,$
A %n ,".*%n) F!#;! "* &! %n#n#n/ !# & ,$#n) =BLM 1+1+4>+
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1.1.1: Revisiting Rates of Change
25-year Walleye Population
Year Walleye Population
0 3000
1 3400
2 3720
3 3976
4 4181
5 4345
6 4476
7 4581
8 4665
9 4732
10 4786
11 4829
12 4863
13 4890
14 4912
15 4930
16 4944
17 4955
18 4964
19 4971
20 4977
21 4982
22 4986
23 4989
24 4991
25 4993
Draining Waterfrom a Hot u!
ime "s# $olume "%#
0 1600
10 1344
20 1111
30 900
40 711
50 544
60 400
70 278
80 178
90 100
100 44
110 11
120 0
& 'ish(tory
A pond was stocked with a type of fish caed !waeye"#The ta$e on the eft %i&es the pop'ation of waeye in thepond fo( the 25 yea(s foowin% the stockin% of the pond"
2"
Do)n the Drain
The p'% is p'ed in a s)a hot t'$" The ta$e onthe (i%ht %i&es the &o')e of wate( in the t'$ f(o)the )o)ent the p'% is p'ed* 'nti it is e)pty"
(our*e:http+,,www"c ips a hoy"co) ,we $ %( a ph ics ,as 0 963"ht)
http://www.clipsahoy.com/webgraphics/as0963.htmhttp://www.clipsahoy.com/webgraphics/as0963.htmhttp://www.clipsahoy.com/webgraphics/as0963.htm
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1.1.1: Revisiting Rates of Change "*ontinue+#
3"
,last -ff
A (ocket isa'nched" The%(aph shows itshei%ht a$o&e the%(o'nd f(o) ti)e of a'nchin% to (et'(nto ea(th"
4"
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1.1.2: hats the Way the ,all ,oun*es/
-e&in d(opped a $a and coected the hei%ht .)/ at &a(io's ti)es .s/" A %(aph of thedata he coected is p(o&ided"
Part &: &verage Rate of Change
-e&in wants to ook at (ate of chan%e of the hei%ht at &a(io's ti)es" He hopes to
dete()ine how 'icky the hei%ht was chan%in% at &a(io's ti)es" -e&in fi(st ooks at thea&e(a%e (ate of chan%e fo( specific ti)e inte(&as" o)pete the ta$e with theinfo()ation in the %(aph"
0nterval Coor+inates of n+ Points &verage
Rate of
AB
B1
12
23
34
45
5H
hat do the &a'es fo( a&e(a%e (ate of chan%e te yo' a$o't the path of the $a andthe speed of the $a
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Part ,: 0nstantaneous Rate of Change
et* -e&in wants to find a point in each inte(&a whose tan%ent has the sa)einstantaneo's (ate of chan%e as each secant"
:ketch a c'(&e of $est fit fo( this data in one coo'( and d(aw the secants fo( theinte(&as in anothe( coo'("
o( each ti)e inte(&a* ocate the point on the %(aph $etween the endpoints whose
tan%ent appea(s to ha&e the sa)e (ate of chan%e as the a&e(a%e (ate of chan%efo( that inte(&a"
1" ;n the inte(&a AB the a&e(a%e (ate of chan%e is " The point whose
tan%ent )atches this (ate of chan%e is . * /" (aw the
instantaneo's (ate of chan%e at this point* if possi$e"
2" ;n the inte(&a B* the a&e(a%e (ate of chan%e is " The point that
)ost cosey )atches this (ate of chan%e is . * /"
3" ;n the inte(&a * the a&e(a%e (ate of chan%e is " The point that
)ost cosey )atches this (ate of chan%e is . * /" (aw the
tan%ent at this point* if possi$e"
4" ;n the inte(&a * the a&e(a%e (ate of chan%e is " The point that
)ost cosey )atches this (ate of chan%e is . * /" (aw the
tan%ent at this point* if possi$e"
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Ref%et'o! o! a(('"!#e!t
T$ ,n,. & !# & ,$#n) % .!$#. $ ,n!#* ,n,. %n %&&!n%#*
,#*,/*/+ I % ; 3 /n5!03#n5%n) #..!8%"#3%n #n "#8%"%'#3%n "$9 #n
$ &/n5#"n3#* $!" & ,#*,/*/09 #"n) $! $%n)+ Y 03/5n30
,n0%03n3*; $# "%0,n,.3%n0 #:/ !# & ,$#n)+
M#n; 03/5n30 $# # .! )!#. & $ ,n,. & !# & ,$#n)9 #n n /.
%n%&;%n) # !# & ,$#n) %$ # *. & # 3#n)n3 *%n ! # ,$! %3$/3 :%n)
#:* /n5!03#n5 % %n # !#*!* ! #*):!#%, ,n3183+
S3/51n30 n ,".#!3"n3#*%' $%! n*)9 #n "#; n !#*%' 3$#3
.%, /,$ #0 $ ,$#%n !/*9 !*# !#9 %".*%,% 5%&&!n3%#3%n9 ,+9 #! #** #:/
!# & ,$#n)+ T$; $# # %&&%,/* %" !,#**%n) $ ,n,. & !# & ,$#n) %n
$ ,n & $ F/n5#"n3#* T$!" & C#*,/*/0+
T$! #! 5%&&!n3 n%n 3$#3 %n* !# & ,$#n) & &/n,%n & @
1+ A!#) !# & ,$#n) & & :n 37 .%n30+
2+ In03#n3#n/0 !# & ,$#n) & & # # .%n3+
3+ A!#) !# & ,$#n) & & :n # #n 9 # # &/n,%n & 8+
4+ In03#n3#n/0 !# & ,$#n) & & # 9 # # &/n,%n & 8+
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7T /n5!03#n5 $% ,n,. .!.!*;9 03/5n30 &%! n $# # *% )!#. &
$ n%n & ,n03#n3 !# & ,$#n)+ S#;%n) 3$#3 n 6/#n3%3; ,$#n) # #
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& n 6/#n3%3; ,!!.n %$ $ #" &!#,%n & $ 33#* ,$#n) & $ $!
6/#n3%3;+ F! #".*9 %& #n :9
.+ 2329 %**/03!#30 $% .!%n,%.*@
I& # .#!%,* % "%n) # # ,n03#n3 !# =.>9 #n % !#* 140 & %n 4
,n9 $n $ 3%" % # !#* #n; %n!#* & *n)$ 1 W 140 K 35 & %
1W 4 K 1 ,n+ S%"%*#!*;9 $ %" %3
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A 31#,$%n) /))%n % / "%n #*n) .#!#*** *%n %n # ,!5%n#35
"#nn!9 :%n) 8.*%,%3 #:/ $ &&! ,!%n# $ "%n+ P$;%,#* "%n9
#n%"#3%n09 #n $! ,"./3!G:#05 * ,#n $*. ,%*%# $% *#!n%n)+
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%$ $% n%n %n .*#,9 $ #!#) !# & ,$#n) & n 6/#n3%3; %$
!., #n$! 5/!%n) #n %n!#* ,#n : %n3!5/,5 # $ ,n03#n3 !# &
,$#n) n,#!; ;%* $ #" n ,$#n) %n $ &/n,%n #*/ ! $
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.!n 3!#*%n) # # ,n03#n3 . & 5 "! .! ,n /* !#* $
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REFERENCES
Ann9 H#!X B%n9 I!*X D#%9 S.$n =F:!/#!; 29 2005>9 Calculus: Early
Transcendentals Single and ultivariable =8$ +>9 N Y!@ %*;9 ISBN 780471
472445
A.*9 T" M+ =/n 167>9 Calculus! "ol# $: %ne&"ariable Calculus 'ith an
ntroduction to inear *lgebra9 4 =2n +>9 %*;9 ISBN 780471000051
A.*9 T" M+ =/n 16>9 Calculus! "ol# +: ulti&"ariable Calculus and inear
*lgebra 'ith *pplications9 4 =2n +>9 %*;9 ISBN 780471000075
C/!#n9 R%,$#!X $n9 F!%' =D,":! 229 18>9 ntroduction to Calculus and *nalysis! "ol# $9 S.!%n)!V!*#)9 ISBN 783540650584
E9 H#! =#n/#!; 29 10>9 *n ntroduction to the ,istory of athematics =6$ +>9
B! C*9 ISBN 78003025584
L#!n9 RnX H*!9 R:! P+X E#!9 B!/, H+ =F:!/#!; 289 2006>9 Calculus:
Early Transcendental -unctions =4$ +>9 H/)$n M%&&*%n C".#n;9 ISBN 780618
606245
S.%#9 M%,$#* =S.":! 14>9 Calculus =3! +>9 P/:*%$ ! P!%$9 ISBN 780
140888
S#!9 #" =D,":! 249 2002>9 Calculus =5$ +>9 B! C*9 ISBN 780534
3337
T$".n9 S%*#n/ P+ =S.":! 89 18>9 Calculus ade Easy =R%9 U.#9
E.#n +>9 N Y!@ S+ M#!%nZ P!9 ISBN 780312185480
$.@+,*%&&n+,"/;[)/%D&%n%%n+.%,A!%,*I309#!%,*I3\
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$.@"#$+/!%#+,",#*,/*/!#&,$#n)+$"*
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